As for activities, you may want to consider these:
1) If there is a medical school nearby, why not ask them if you can set up a mentorship program? My school runs one with a local high school and a local undergraduate university, and the medical students get pretty excited about it. 🙂
2) You could invite local physicians to a question and answer panel at your school.
3) You could organize volunteer outings (not directly medical, but still important)
4) You could hold a fundraiser and purchase medical supplies for a local free clinic with the profits.
5) You could provide information packets to your members about the medical school application process.
6) If you are feeling ambitious (and your local hospital is generous) you could set up a shadowing program.
Hope that gives you a few ideas to start with. Good luck.
PS - if you are not a medical student, your status should not be "medical student"